A new approach of B-spline wavelets to solve fractional differential equations.

This paper presents a groundbreaking method for solving the multi-order fractional differential (M-OFD), both linear and nonlinear, as well as fractional partial differential equations (FPDE)s. This approach involves constructing an operational matrix of fractional derivatives using linear B-spline (LB-S) wavelet functions with perfect subtlety. The new method has two crucial features. Firstly, it simplifies the problem by converting it into a set of algebraic equations, which is a significant advantage. This makes the method highly accurate and reliable. Secondly, it uses thresholding to dramatically reduce the computational workload in linear problems. This leads to lightning-fast and highly efficient problem-solving. The newly developed scheme underwent a thorough examination of its error estimates and convergence, revealing remarkable results in terms of accuracy and efficiency. The analysis provides a comprehensive understanding of the scheme's performance, highlighting its potential as a dependable and effective method. Based on the findings, it is evident that the proposed method not only delivers exceptional precision but also operates with remarkable efficiency. • The fractional differential equations are considered in the current work. • A numerical technique based on linear B-Spline wavelets is used to find its numerical solution. • Also the constructing the operational matrix of fractional derivative based of wavelets is main goal. • Thus the main problem is reduced to sparse problem of solving a system of algebraic equations. • The method is examined on several real and test examples of various types to show its efficiency. [ABSTRACT FROM AUTHOR]